It seems to me rather difficult for writers to create good books on this subject.
Some years ago I thought there were no such books at all.
There are many reasons: it is difficult to describe the
process of discovery and describe it in the exciting way.
The subject has narrow audience and not the way to make best-seller...

Comments on how authors try to avoid these problems are also welcome.
The movie "A Beautiful Mind" is a (beautiful for me) example, where the story of mathematician was mixed with love and spy stories to make it interesting for general
audience, well not so much preserved from mathematician's story, but nevertheless
I am quite positive about it.

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5

I think 'other scientists' should be removed; or at least it should be narrowed down to 'scientists in closely related fields'. To collect books featuring, say, a microbiologist seems totally off-topic for MO to me.
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quidJul 8 '12 at 11:43

5

I'm going to take the liberty of removing "scientists" from the question since there are way too many books about scientists to ask for a list, and it makes more sense to ask about books featuring mathematicians on MO.
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Douglas ZareJul 8 '12 at 20:59

5

It is perhaps worth pointing out that while the movie "A Beautiful Mind" was fictionalized in many ways, the book it is based on is non-fiction. It is an (as far as I could tell) well-researched biography of the very real John Nash.
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Noah SteinJul 9 '12 at 14:38

10

Mathematicians should not do, and certainly not enjoy, anything other than mathematical research, lest they give themselves away as human beings with a variety of interests and not a 100% devotion to just the one.
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Sridhar RameshJul 10 '12 at 16:43

7

"Time spent reading is time not not used for doing research." @Harry: are you an intuitionist?
–
Margaret FriedlandJul 10 '12 at 17:52

65 Answers
65

The Man Without Qualities (Der Mann ohne Eigenschaften) by Robert Musil. The protagonist is a Mathematician, and the book runs through an amazing range of issues concerning science, technology and their relations to society and to the nature of consciousness. It is set in the last days of the Austro-Hungarian Empire. The novel was never finished -- the published fragment runs to around 1700 pages.

There is a graphic novel called Logicomix, by Apostolos Doxiadis and Christos Papadimitriou, which is about Bertrand Russell and the search for the foundations of mathematics. I know you were asking for fiction, but as with Kepler, this is sort of a fictionalized version of actual events, rather than an academic history book. Plus the pictures are great! And it's self-referential; the authors themselves appear in the book.

Uncle Petros and Goldbach's conjecture is a story about a fictitious mathematician who became obsessed with solving the Goldbach's conjecture. The main theme of the book is obsession and it is quite engaging. It also has the mathematicians Ramanujan, Hardy, Littlewood, Turing, etc. as characters.

If you take the question literally then Asimov's short story Mirror image would also come here. This story features two mathematicians disagreeing on the priorty of a discovery. We, however, see very little of the mathematicians and none of the mathematics. Mathematicians as opposed to lesser scientists were used in the story because that lets them do work alone without complicated equipment or laboratory assistants, useful for the purposes of the story.
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Zsbán AmbrusJul 8 '12 at 20:17

2

@Federico Poloni: I learned my lesson at the Newtonian physics camps - they always went through springs and falls.
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Zack WolskeJul 9 '12 at 7:50

Cryptonomicon is a book by Neal Stephenson. One of the main characters in the WWII timeline is Lawrence Waterhouse, a mathematician and cryptologist. Waterhouse gets to interact with Alan Turing.

Neal Stephenson later wrote a series (the Baroque cycle, starting with Quicksilver) which featured ancestors of the characters in Cryptonomicon. The Waterhouse in Quicksilver works with Isaac Newton and encounters Leibniz, but is not a mathematician.

(I don't think either of these works is as good as Stephenson's Snow Crash, but that doesn't feature mathematicians.)

"Proof" is a play, but it is based upon a women finishing a proof that her father was unsuccessfully working on as he slips into mental decline. In fact, the play has done quite well, and they even made a movie version with Gwenneth Paltrow, Anthony Hopkins and Jake Gyllenhall.

When you mention the audience being narrow and adding other elements to attract a larger spectrum of the population, I would amend your comment about spies and intrigue to note that a majority of the "popular" novels and movies about mathematicians involve mental illness as a "lead" character. Also true in "A Beautiful Mind". One could argue the same for "Flatland," but the interactions of the main character are a little more "antisocial" than "mentally ill," per se.

I recommend The Man Who Counted, an amazing fiction book about a fictitious mathematician called Beremiz Samir and a traveler called Malba Tahan.

The first two chapters tell how Malba Tahan was traveling from Samarra to Baghdad when he met Beremiz Samir, a young lad with amazing mathematical abilities. The traveler then invited Beremiz to come with him to Baghdad, where a man with his abilities will certainly find profitable employment. The rest of the book tells various incidents that befell the two men along the road and in Baghdad. In all those events, Beremiz Samir uses his abilities with calculation like a magic wand to amaze and entertain people, settle disputes, and find wise and just solutions to seemingly unsolvable problems.
In the first incident along their trip (chapter III), Beremiz settles a heated inheritance dispute between three brothers. Their father had left them 35 camels, of which 1/2 (17.5 camels) should go to his eldest son, 1/3 (11.666... camels) to the middle one, and 1/9 (3.888... camels) to the youngest. To solve brother's dilemma, Beremiz convinces Malba to donate his only camel to the dead man's estate. Then, with 36 camels, Beremiz gives 18, 12, and 4 animals to the three heirs, making all of them profit with the new share. Of the remaining two camels, one is returned to Malba, and the other is claimed by Beremiz as his reward.

Greg Egan is a science-fiction writer that holds a B.S. in Mathematics (and has co-authored a paper with John Baez). He often manages to insert some advanced maths, physics and computer science content in his novels: for instance, listing only mathematics, fiber bundles in Diaspora, Einstein's equation for general relativity in Incandescence, Cantor sets and commutative hypercubes in the short stories The Infinite Assassin and Glory.

His story Dark Integers deserves special mention; it is a sequel to Luminous, best read in order.

It is truly science fiction written for scientists and mathematicians in particular; they are the only readers that are able to grasp fully both the casual references to advanced mathematical content and the grand ideas underlying his stories. Even after a master in pure maths and a phd in numerical analysis, often I feel that I do not know enough geometry and theoretical physics to get all the facets and implications of what he writes.

This feature sets him apart from most other writers in this list, who address maths from a popular-science point of view.

On the top of my head, I find it difficult to name a novel of his that does not feature a scientist among the protagonists.

The story -perhaps there are more, but at least a story- involving Cantor sets is The Infinite Assassin, the first story in Axiomatics. The short story Glory (which you can read online, along with Dark Integers, both are linked from his Wikipedia entry) involves not just a commutative square, but a higher dimensional commutative hypercube (tell your categorically minded colleagues!).
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Zack WolskeJul 9 '12 at 5:48

Someone else mentioned Hari Seldon in Asimov's Foundation Series, but there is also a wonderful Asimov short story in which the protagonist is a government mathematician who discovers, by analyzing primitive computers, how to do computations such as multiplication and division with only paper and pencil. (Actually, he may be writing on a pad, but anyway, he's doing it by hand.)

SPOILER ALERT (The rest of this post gives away some, but not all, of the plot.)

The point of the story is that no one on earth remembers how to do even arithmetic, everyone just relies on calculators and computers. The government becomes very interested in this discovery, because it has the potential to allow them to build war rockets piloted by people (inexpensive), rather than by computers (expensive). Given the extent to which children these days are taught to do arithmetic using calculators, Asimov's story is quite prescient. The only problem is that I don't remember the title, maybe someone on MO can help out with that.

I think that many, if not all, short stories of Jorge Luis Borges qualify. Even if they're not directly about maths, they often involve some kind of strange "mathematical structure", like paradoxes, symmetries, mirrors, labyrinth, distortions of space and time. Also, the notion of infinity is a common topic of these stories: the most well known example is "The library of Babel", but there are many other examples like "The immortal" or "Aleph" (which is of course a reference to the standard notation for transfinite numbers).

Borges is too good, a must read! "the library of Babel" often gets me to think about infinity, since the problem posed there was in fact finite, but "sensorially infinite".
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Yul OtaniJul 10 '12 at 17:38

I read this book and felt that it had far too many wandering intellectual digressions to be popular in most countries. If I weren't a mathematician, I doubt that I would have been able to get through the whole book. When I learned that it was popular in France, I was tempted to say, "Only in France!"
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Timothy ChowJul 9 '12 at 3:18

He is a man of good birth and excellent education, endowed by nature with a phenomenal mathematical faculty. At the age of twenty-one he wrote a treatise upon the binomial theorem which has had a European vogue. On the strength of it, he won the mathematical chair at one of our smaller universities, and had, to all appearances, a most brilliant career before him. But the man had hereditary tendencies of the most diabolical kind. A criminal strain ran in his blood, which, instead of being modified, was increased and rendered infinitely more dangerous by his extraordinary mental powers. Dark rumours gathered round him in the University town, and eventually he was compelled to resign his chair and come down to London. He is the Napoleon of crime, Watson. He is the organiser of half that is evil and of nearly all that is undetected in this great city...
—Holmes, "The Final Problem"

He is the celebrated author of "The Dynamics of an Asteroid", a book
which ascends to such rarefied heights
of pure mathematics that it is said
that there was no man in the
scientific press capable of
criticizing it.

He was also an early exponent of the
subject of Game Theory, well in
advance of Nash and Von Neumann. Oskar
Morgenstern analysed his contributions
in [3].

I recommend The Number Devil, an amazing book for small children about a boy bored with mathematics who is approached in his dreams by a little red man, the number devil, who teaches him mathematics. Although a children's book, I think this certainly counts.

Another play, "Arcadia" by Tom Stoppard. One of the main characters is Thomasina Coverly, "a precocious teenager with ideas about mathematics well ahead of her time" (to quote from Wikipedia). It is not too much of a spoiler to reveal that this fictional young woman came up with what we now call fractals.

Thomas Pynchon's "Against the Day" has several characters who are mathematicians, with some of the action taking place in Goettingen in the early twentieth century. There are many mathematics references and jokes throughout the book which only mathematicians would get.

Measuring the World recreates the parallel but contrasting lives of two geniuses of the German Enlightenment - the naturalist and explorer Alexander von Humboldt and the mathematician and physicist Carl Friedrich Gauss. Towards the end of the 18th century, these two brilliant young Germans set out to measure the world. Humboldt, a Prussian aristocrat schooled for greatness, negotiates savannah and jungle, travels down the Orinoco, climbs the highest mountain known to man, counts head lice, and explores every hole in the ground. Gauss, a man born in poverty who will be recognized as the greatest mathematician since Newton, does not even need to leave his home in Gottingen to know that space is curved. He can run prime numbers in his head, cannot imagine a life without women and yet jumps out of bed on his wedding night to jot down a mathematical formula."

"His Master's Voice" is a novel about scientists who receive the message from extraterrestrial civilization and try to decipher it. The narrator of the story is a mathematician named Peter Hogarth.

Another great book by Lem in which you can find a lot of reference to mathematics is "The Cyberiad", a series of short, humorous stories about adventures of two constructors, Trurl and Klapaucius. "The dragons of probability" is a masterpiece!

In one of the stories of "The Cyberiad" Trurl constructs a machine to compose verse. One of the poems is a love poem using mathematical terms (almost exclusively).
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Margaret FriedlandAug 28 '12 at 14:19

1

... and is one of the readings when I got married.
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Willie WongOct 4 '12 at 11:23

Kepler by John Banville is a sort of 'fictional biography'. Banville is a Booker prize winner, very highly regarded. His prose is some of the most beautiful, dense and lyrical I've ever read, and I'd recommend Kepler to anyone with an interest in mathematics and a taste for masterful writing.

"The Peace War" by Vernor Vinge had a rather nice passage about the coming-of-age of a teenage math whiz, self-taught until meeting up with an established mathematician (shades of Ramanujan-Hardy). Excerpt:

Wili spent a week dreaming
up other orthogonal families and was
disappointed to discover that most of
them were al­ready famous - haar
waves, trig waves - and that others
were special cases of general families
known for more than two hundred years.
He was ready for Naismith's books now.
He dived into them, rushed past the
preliminary chapters, pushed himself
toward the frontier where any new
insights would be beyond the farthest
reach of previous explorers.

In the
outside world, in the fields and the
forest that now were such a small part
of his consciousness, summer moved
into fall. They worked longer hours,
to get what crops remained into
storage before the frosts. ...

While those two are major characters in the book, it doesn't get mathematical like that much more that I remember (it's been quite a few years since I read it).

The Last Theorem by Arthur C Clarke and Frederik Pohl (and the late Clarke's final book). The main character is a young Sri Lankan mathematician who isn't satisfied with Wiles' proof of Fermat's Last Theorem. There is a reasonable amount of discussion of mathematics for a mass-market science fiction novel, if I recall correctly.

John Banville is perhaps the best stylist I've ever read. His style is poetic, concise (few of his books are much over 200 pages), perhaps even mathematical. Many of his protagonists are mathematicians, but that might not make a great deal of difference to this community as mathematics is usually discussed only in passing. Banville has a lot to say about the creative experience and travails of being a mathematician, but if you're looking for, say, witty insights about topology, best look elsewhere.

Banville's work with the most to say about the general experience of being a mathematician is Mefisto. The protagonist is a mathematician, probably a chaos theorist. Mefisto never goes into the details of his work, but nearly every word is a reflection on the working style of a mathematician and the necessary conditions for great discoveries to occur. The book shares some themes with Aranofsky's movie Pi. Mefisto is loosely based on Faust.

Banville's fictionalized biographies of Copernicus and Kepler contain his greatest scientific detail. Personally, I slightly prefer Doctor Copernicus, though Kepler is also very good, particularly the passages about Kepler's battles with his patron Tycho Brahe over geo-heliocentrism. Doctor Copernicus contains some absolutely beautiful passages about the process of doing science, and the details of Copernicus' life, both real and fictionalized, are fascinating.

The protagonist of The Newton Letter is a historian studying Newton's nervous breakdown. Parallels between Newton's experiences and the historian's begin to emerge.

The protagonist of The Book of Evidence is a statistician turned murderer and art thief. Statistics isn't discussed much, though there are a few snappy lines about what qualities make a good mathematician. I haven't read Ghosts, but, apparently, Ghosts has the same characters as The Book of Evidence.

Banville's most recent book, The Infinities, is about a son's return to the deathbed of his father, a famous mathematical physicist. The book has little to say about math: more to say about celebrity, I think. Pretty much everything mentioned about math is deliberately counterfactual. For example, it's mentioned in passing that cold fusion is a reality, and that the father got famous for his general equations explaining why it works.

The two books I particularly recommend to scientists are Doctor Copernicus and Mefisto.

In the short story Division by Zero by Ted Chiang, a mathematician discovers a proof that 1=2. The story discusses (among other things) its effect on her, but other (real-life) mathematicians and their ideas are also mentioned.